By Cauchy the word “symmetric,” as applied to functions, was used in a more general sense than that in which we ordinarily use it now, or than that in which it was used before his time. He spoke of “fonctions symétriques permanentes” and “fonctions symétriques alternées:” we apply the word symmetric only to certain of the first of these; the second we call simply “alternating functions.” Thus the expression

was called by him a permanent symmetric function, since if a1, a2, a3 are interchanged in order with b1, b2, b3, the function remains unaltered. It would be more definite to say that it is a permanent symmetric function with respect to a1, a2, a3 and b1, b2, b3.